Collisional interaction limits between dark matter particles and baryons in `cooling flow' clusters

Presuming weak collisional interactions to exchange the kinetic energy between dark matter and baryonic matter in a galaxy cluster, we re-examine the effectiveness of this process in several `cooling flow' galaxy clusters using available X-ray observations and infer an upper limit on the heavy dark matter particle (DMP)-proton cross-section σ<sub>xp</sub>. With a relative collisional velocity V-dependent power-law form of σ<sub>xp</sub> = σ<sub>0</sub>(V/10<sup>3</sup>kms<sup>-1</sup>)<sup>a</sup> where a <= 0, our inferred upper limit is σ<sub>0</sub>/m<sub>x</sub> <~ 2 × 10<sup>-25</sup>cm<sup>2</sup>GeV<sup>-1</sup> with m<sub>x</sub> being the DMP mass. Based on a simple stability analysis of the thermal energy balance equation, we argue that the mechanism of DMP-baryon collisional interactions is unlikely to be a stable non-gravitational heating source of intracluster medium (ICM) in inner core regions of `cooling flow' galaxy clusters.